Question: Complete the equation. $\dfrac54+ \dfrac54~=~$
Solution: Let's figure out what $\dfrac{5}{4} + \dfrac{5}{4}$ equals. $\dfrac{0}{4}$ $\dfrac{5}{4}$ $\dfrac{10}{4}$ $\llap{{+}}\!\frac{5}{4}$ $\llap{{+}}\!\frac{5}{4}$ $\dfrac{5}{4}+ \dfrac{5}{4} = \dfrac{10}{4}$ Now, let's figure out how many times we add $\dfrac{1}{4}$ to make $\dfrac{10}{4}$. $\dfrac{0}{4}$ $\dfrac{1}{4}$ $\dfrac{2}{4}$ $\dfrac{3}{4}$ $\dfrac{4}{4}$ $\dfrac{5}{4}$ $\dfrac{6}{4}$ $\dfrac{7}{4}$ $\dfrac{8}{4}$ $\dfrac{9}{4}$ $\dfrac{10}{4}$ $\llap{{+}}\!\frac{1}{4}$ $\llap{{+}}\!\frac{1}{4}$ $\llap{{+}}\!\frac{1}{4}$ $\llap{{+}}\!\frac{1}{4}$ $\llap{{+}}\!\frac{1}{4}$ $\llap{{+}}\!\frac{1}{4}$ $\llap{{+}}\!\frac{1}{4}$ $\llap{{+}}\!\frac{1}{4}$ $\llap{{+}}\!\frac{1}{4}$ $\llap{{+}}\!\frac{1}{4}$ $=\overbrace{{\dfrac1{4}} +{\dfrac1{4}} +{\dfrac1{4}} + {\dfrac1{4}} +{\dfrac1{4}} +{\dfrac1{4}} +{\dfrac1{4}} +{\dfrac1{4}} +{\dfrac1{4}} + {\dfrac1{4}}}^{{10}\text{ fourths}} $ $=\dfrac{{10}\times{1}}{{4}}$ $\dfrac{5}{4}+ \dfrac{5}{4} = {10} \times \dfrac14$